Solving Trigonometry Problems

Tags: How To Write A Precis EssayMy Favorite Food EssaysMy Most Embarrassing Moment EssayTitle Proposal For Research PaperUnforgettable Place EssayDuke Dissertation ScandalSetting Essay On The Yellow WallpaperPersuasive Essay On International AdoptionTypes Of Reasoning In Critical Thinking

$$\displaystyle \beginx \frac=\frac\,\,\,\,\,\,\,\,\,\,\,\,x \frac=\frac\\\,\,\,x=-\frac\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=\frac\end$$ Note that (by looking at Unit Circle) this can be simplified to $$\displaystyle \$$ (Remember that you add $$\pi k$$ instead of $$2\pi k$$ for tan and cot).

$$\displaystyle \begin\frac=\sin \theta \cos \theta \\\cos \theta =4\theta \cos \theta \\4\theta \cos \theta -\cos \theta =0\\\cos \theta \left( \right)=0\\\cos \theta \left( \right)\left( \right)=0\\\cos \theta =0\text\,\,\text\,\,\sin \theta =\pm \frac\,\\\\\\end$$ Note that you can check these in a graphing calculator (radian mode) by putting the left-hand side of the equation into  and the right-hand side into  and get the intersection.

Note that $$k$$ represents all integers $$\left( k\in \mathbb \right)$$.

Note also that I’m using “fancy” notation; you may not be required to do this., depending on your book or teacher.

You won’t get the exact answers, but you can still compare to the exact answers you got above. This is because we could have fewer or more solutions in the Unit Circle, and thus for all real solutions when we add the $$2\pi k$$ or $$\pi k$$.

So when we solve these types of trig problems, we always want to solve for the General Solution first (even if we’re asked to get the solutions between solutions.Let’s start out with solving fairly simple Trig Equations and getting the solutions from $$\left[ 0,2\pi \right)$$, or $$\left[ \right)$$.Here is the Unit Circle again so we can “pick off” the answers from it: Notice how sometimes we have to divide up the equation into two separate equations, like when the argument of the trig function is an expression, like $$\displaystyle \theta \frac$$.If we want $$\displaystyle \left( \right)$$ for example, like in the The Inverse Trigonometric Functions section, we only pick the answers from Quadrants I and IV, so we get $$\displaystyle \frac$$ only.But if we are solving $$\displaystyle \sin \left( x \right)=\frac$$ we get $$\displaystyle \frac$$ and $$\displaystyle \frac$$ in the interval ; there are no domain restrictions.As another example, for $$\cos \left( \frac \right)$$, we’ll only get one solution instead of the normal two.Let’s do some problems, finding the general solutions first, and then finding the solutions in the interval.We learned how to factor Quadratic Equations in the Solving Quadratics by Factoring and Completing the Square section.Note that when we factor trig equations to find solutions, like we do with “regular” equations, we never just divide a factor out from each side.$$\displaystyle \begin\tan \left( \right)=1\\frac \frac=\frac\,\,\,\,\,\,\,\,\,\,\frac \frac=\frac\\,\,\,\frac=-\frac\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac=\frac\\,\,\,\theta =-\frac\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\theta =\frac\end$$ Since trig functions go on and on in both directions of the $$x$$-axis, we’ll also have to know how to solve trig equations over the set of real numbers; this is called finding the general solutions for these equations.We still use the Unit Circle to do this, but we have to think about adding and subtracting multiples of $$2\pi$$ for the sin, cos, csc, and sec functions (since $$2\pi$$ is the period for them), and $$\pi$$for the tan and cot functions (since $$\pi$$ is the period for them).

• Trigonometry Problem Solver - com

The Trigonometry Problem Solver is a user-friendly program for solving various trigonometry problems that you enter. Its capability to show step-by-step solutions with formulas used and.…

• SOLVING TRIGONOMETRIC EQUATIONS - S. O. S. Math

This site was built to accommodate the needs of students. The topics and problems are what students ask for. We ask students to help in the editing so that future viewers will access a cleaner site. If you feel that some of the material in this section is ambiguous or needs more clarification, please let us know by e-mail. Trigonometry…

• Solving Trigonometric Equations – She Loves Math

Solving Trigonometric Equations – General Solutions. Since trig functions go on and on in both directions of the \x\-axis, we’ll also have to know how to solve trig equations over the set of real numbers; this is called finding the general solutions for these equations.…

• Solving right triangles. Topics in trigonometry.

SOLVING RIGHT TRIANGLES. This is a topic in traditional trigonometry. It does not come up in calculus. To SOLVE A TRIANGLE means to know all three sides and all three angles. When we know the ratios of the sides, we use the method of similar figures. That is the method to use when solving an isosceles right triangle or a 30°-60°-90° triangle.…

• Solve Trigonometry Problems Online Trigonometry Homework

The thing about math is you need to understand the concepts or else it will be tough to get good grades. H2 We Can Do Your Trigonometry Homework – We Solve Trigonometry Problems with Solutions Trigonometry studies the relationship involving lengths and angles of triangles. When you look at it this way, it sounds like a simple math topic.…

• Applications of Right Triangles and Trig Functions

Trigonometry Word Problems Solutions 1 One diagonal of a rhombus makes an angle of 29 with a side ofthe rhombus. If each side of the rhombus has a length of 7.2", find the lengths of the diagonals. Draw a sketch 7.2" Label the rest 7.2" Solve 7.2" Since it is a rhombus, we know all the sides are 7.2". The opposite angles are congruent…

• Trigonometry Examples - Mathway Math Problem Solver

Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.…